TY - JOUR
T1 - Construction of a family of Moufang loops
AU - Curtis, Robert
PY - 2007/3/1
Y1 - 2007/3/1
N2 - This paper is an excerpt from a Rayleigh essay submitted at the University of Cambridge in January 1970. We reproduce it now as it gives a general construction of a family of Moufang loops to which all bar one of the finite subloops of the Cayley algebra O belong. These subloops were classified up to isomorphism in the original essay, but are classified up to equivalence under the action of the group of symmetries of O in Boddington and Rumynin [1]. Explicitly, given a group G with an element a such that a(2) = 1 in its centre, we construct a Moufang group G in which G has index 2. G will be non-associative unless G is abelian.
AB - This paper is an excerpt from a Rayleigh essay submitted at the University of Cambridge in January 1970. We reproduce it now as it gives a general construction of a family of Moufang loops to which all bar one of the finite subloops of the Cayley algebra O belong. These subloops were classified up to isomorphism in the original essay, but are classified up to equivalence under the action of the group of symmetries of O in Boddington and Rumynin [1]. Explicitly, given a group G with an element a such that a(2) = 1 in its centre, we construct a Moufang group G in which G has index 2. G will be non-associative unless G is abelian.
UR - http://www.scopus.com/inward/record.url?scp=34247874543&partnerID=8YFLogxK
U2 - 10.1017/S0305004106009789
DO - 10.1017/S0305004106009789
M3 - Article
SN - 1469-8064
VL - 142
SP - 233
EP - 248
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
ER -